Exercise 14.5.2 Consider a vertical plane Π (i.e. parallel to the z-axis) which passes through the points (1, 3, 0) and (1, 5, 2).
(a) Find a vector parametric equation for Π in the form r = p + sv + tw.
(b) Considering the cross product of the vectors v and w, or otherwise, find a Cartesian equation for Π in the form
ax + by + cz = d
for some constants a, b, c, d to be determined.
(c) Confirm that the points (1, 3, 0) and (1, 5, 2) both satisfy the Cartesian equation obtained in part (b) and that this Cartesian equation indeed describes a plane that is vertical